Advanced Particle Physics: Leptons and Quarks

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Questions and Answers

What is the primary focus of the research presented in the document?

  • The properties of gravitational waves
  • The mechanism of dark matter interactions
  • The history of particle physics development
  • Explaining the mass ratios of leptons and quarks (correct)

What challenge does the research address regarding Yukawa couplings?

  • Their independence from the Higgs VEV
  • Their relation to the speed of light
  • Their arbitrary nature in the Standard Model Higgs mechanism (correct)
  • Their experimental verification in particle collisions

How many generations or families of leptons and quarks are discussed in the document?

  • One
  • Two
  • Four
  • Three (correct)

What phenomenon is responsible for mass generation of W and Z gauge bosons according to the Standard Model?

<p>Electroweak symmetry breaking (C)</p> Signup and view all the answers

What is proposed in the document concerning neutrino mass eigenstates?

<p>Predictions for all three left-chiral mass eigenstates (D)</p> Signup and view all the answers

What is one reason for the existence of three generations of particles?

<p>They arise from symmetries in the equations. (C)</p> Signup and view all the answers

How does the new equation discussed differ from the Koide formula?

<p>It does not treat particle masses as constants. (C)</p> Signup and view all the answers

What is one application of the new equation proposed?

<p>In the U(1)B−L symmetry framework. (C)</p> Signup and view all the answers

What does the new equation successfully predict regarding neutrinos?

<p>The mass eigenstates of all three left-handed neutrinos. (A)</p> Signup and view all the answers

Why are the masses of up and down quarks significant?

<p>Their masses were previously explained but now are understood under new frameworks. (B)</p> Signup and view all the answers

What does the quantum number ng represent?

<p>Number of generations or families (A)</p> Signup and view all the answers

Which variable is used to represent the fermion spin quantum number?

<p>S (D)</p> Signup and view all the answers

What is the equation used to define the quantum number nYw?

<p>nYw = [(2 ∙ T3 − Qe) + Yw ∙ αG(Q)] / (B − L) (B)</p> Signup and view all the answers

What approximation is made regarding the gravitational coupling αG(Q) for most particles?

<p>It is approximated to zero (B)</p> Signup and view all the answers

Which of the following particles has a non-zero value for the gravitational coupling αG(Q)?

<p>Right-handed neutrinos (C)</p> Signup and view all the answers

In the equation for nYw, what do the variables B and L respectively represent?

<p>Baryon number and lepton number (B)</p> Signup and view all the answers

What is the reciprocal Fibonacci constant represented by in the context?

<p>Ψ (C)</p> Signup and view all the answers

Which of the following is true about the quantum number п?

<p>It includes unstable particles and their anti-particles (A)</p> Signup and view all the answers

What is the lepton quantum number for all leptons?

<p>1 (A)</p> Signup and view all the answers

What weak hypercharge do all left-chiral leptons have?

<p>−1 (C)</p> Signup and view all the answers

What is the charge quantum number for charged leptons?

<p>−1 (B)</p> Signup and view all the answers

Which type of leptons have a weak isospin T3 = −1/2?

<p>Left-chiral charged leptons (B)</p> Signup and view all the answers

What is the weak hypercharge of right-chiral charged leptons?

<p>−2 (B)</p> Signup and view all the answers

Which type of leptons have no weak isospin or weak hypercharge?

<p>Right-chiral neutrinos (C)</p> Signup and view all the answers

In the provided equations, what does Qe represent?

<p>Charge quantum number (B)</p> Signup and view all the answers

Which equation defines c4 in relation to Qe and other variables?

<p>$c4 = \frac{2 \cdot Qe \cdot S [Qe + (B + L)]}{(B - L)}$ (D)</p> Signup and view all the answers

What does the value of $\alpha(Q)$ depend on according to the neutrino equation?

<p>The generation/family number N of neutrinos (B)</p> Signup and view all the answers

What is the experimental upper limit for the sum of all three neutrino mass eigenstates?

<p>0.09 eV ∙ c−2 (B)</p> Signup and view all the answers

Which statement is true regarding the mass hierarchy of left-handed neutrinos?

<p>They have an inverse mass hierarchy. (B)</p> Signup and view all the answers

In the context of neutrinos, what does the equation state regarding anti-neutrinos?

<p>They have the same Yukawa couplings and masses as neutrinos. (D)</p> Signup and view all the answers

What is stated about right-chiral neutrinos in relation to their existence?

<p>They are sterile if they exist. (D)</p> Signup and view all the answers

What is mentioned regarding the mass of right-chiral neutrinos?

<p>They have a colossal mass. (D)</p> Signup and view all the answers

What does the neutrino equation imply about the masses of neutrinos?

<p>Neutrino masses depend on their respective generation/family number. (B)</p> Signup and view all the answers

Why does the variable $\alpha_G(Q)$ not need to be calculated?

<p>It is not equal to zero or very close to zero. (C)</p> Signup and view all the answers

What is the charge quantum number for up-type quarks?

<p>2/3 (D)</p> Signup and view all the answers

What weak isospin value do right-handed d-type quarks have?

<p>0 (D)</p> Signup and view all the answers

In the formula for up quarks, what does the term sin²θW(Mu) represent?

<p>The Weinberg angle for up quarks (D)</p> Signup and view all the answers

What is the primary characteristic of all u-type quarks compared to their anti-particles?

<p>They have opposite charge quantum numbers. (D)</p> Signup and view all the answers

What is the value of weak isospin T3 for left-handed d-type quarks?

<p>1/2 (C)</p> Signup and view all the answers

How is the value of α for up quarks estimated in the formula?

<p>α is approximated as α(mu). (D)</p> Signup and view all the answers

Which quark parameter includes the term 6π in its formula?

<p>The Yukawa coupling (A)</p> Signup and view all the answers

What does the value for MN represent in the context of quarks?

<p>The mass of quarks (A)</p> Signup and view all the answers

Flashcards

Generations of Leptons and Quarks

The Standard Model classifies fundamental particles into three generations, each containing a lepton and quark pair.

Mass Ratios of Leptons and Quarks

The paper aims to explain the observed mass ratios between the particles of different generations.

Yukawa Couplings

Parameters in the Standard Model that determine the strength of the interaction between Higgs bosons and fermions (leptons and quarks).

Higgs Vacuum Expectation Value (VEV)

A specific value needed for the Higgs mechanism to function and which affects mass calculations, crucially relating to the value of Yukawa coupling.

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Electroweak Symmetry Breaking

A process where the electroweak force splits into the electromagnetic and weak forces, giving mass to particles.

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Mass Eigenstates of Neutrinos

The paper will predict the mass values of different types of neutrinos.

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Standard Model of Particle Physics

A framework that describes the fundamental forces and particles of nature, excluding gravity.

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Lepton Quantum Number (L)

A quantum number that distinguishes leptons from antileptons. Leptons have L = 1, and antileptons have L = -1.

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Weak Hypercharge (Yw) of Left-Chiral Leptons

The weak hypercharge of left-chiral leptons is -1.

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Weak Hypercharge (Yw) of Right-Chiral Charged Leptons

The weak hypercharge of right-chiral charged leptons is -2.

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Weak Isospin (T3) of Left-Chiral Charged Leptons

The weak isospin of left-chiral charged leptons is -1/2.

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Weak Isospin of Right-Chiral Charged Leptons

The weak isospin of right-chiral charged leptons is 0.

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Charge Quantum Number (Qe)

The electric charge of leptons. Charged leptons have Qe = -1. Antileptons have Qe = +1

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Sterile Neutrinos

Hypothetical neutrinos that do not interact through the weak force.

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c1, c2, c3, c4

Constants or variables in particle physics calculations.

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Equation 13 (c2 calculation)

A formula relating the constant c2 to parameters (S,Qe,B,L) related to particle behavior.

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Equation 14 (c3 calculation)

A formula relating the constant c3 to parameters (N,S,Qe,B,L) related to particle behavior.

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Equation 15 (c4 calculation)

A formula relating the constant c4 to parameters (S,Qe,B,L) related to particle behavior.

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d-type quark parameters

Calculated values of various parameters associated with d-type quarks, excluding the fine-structure constant α.

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d-type quark Yukawa couplings and masses

Calculated values for the strengths of interactions between d-type quarks and the Higgs boson, along with their respective masses.

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Up-type quarks charge Q

Have a charge quantum number Q = +2/3, opposite to their antiparticles.

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d-type quark weak isospin T3

1/2 for left-handed quarks; 0 for right-handed quarks.

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Up quark formula (λu)

A formula calculating Yukawa couplings (λu) for up quarks, dependent on fine-structure constant (α), Weinberg angle (θW), and mass (Mu).

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Neutrino Mass Dependence

Neutrino masses depend on their generation number (family) N, not other factors.

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Neutrino Mass Hierarchy (Left-Chiral)

Left-handed neutrinos have an inverse mass hierarchy compared to charged leptons.

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Neutrino Mass Limit (Experimental)

Experimental upper limit on the sum of all three neutrino masses is 0.09 eV/c².

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Neutrino Oscillations

Neutrinos change flavor during travel – proving they have mass.

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Right-Chiral Neutrinos (Sterile)

If right-handed neutrinos exist, they must be 'sterile' due to their massive nature.

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α(Q) Value

The value of α parameter relating to fine structure constant and cannot be less than fine structure constant value.

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Yukawa Couplings

Parameters in the Standard Model that determine the strength of interactions between Higgs bosons and fermions (leptons and quarks).

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λνf

Parameter representing left-handed neutrino Yukawa couplings in equation (23)

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Particle Generations

The Standard Model groups fundamental particles into three families (generations), each with a lepton and quark pair.

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Reduced Planck constant

Removed from equations using natural units.

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Mass Ratios (Particles)

The paper explores why particles in different generations have different masses.

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Δq (unstable particles)

Different values for each unstable particle.

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Weinberg Angle Measurement

A method to determine the Weinberg angle, a fundamental parameter in the Standard Model, using low-energy lepton/quark interactions.

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f = l

Lepton and quark flavors are equal.

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ng (generations)

Number of fermion families (3).

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Quark Mass Explanation

The paper offers an explanation for why up and down quarks have specific masses.

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Koide Formula Limitation

The Koide formula, a prior approach to explaining particle masses, had limitations in treating particle masses as constant.

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nf (flavors)

Number of fermion flavors (6).

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Neutrino Mass Eigenstates

The paper predicts the mass values of the three types of neutrinos.

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S (fermion spin)

Quantum number for fermion spin (1/2).

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nYw (weak hypercharge particles)

Number of particles interacting via weak hypercharge.

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Sterile Neutrinos

The paper makes predictions about the maximum possible mass for a type of hypothetical neutrino.

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B-L Symmetry

This new equation might be applicable to a particular symmetry, or potential related symmetries in particle physics.

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Yw (weak hypercharge)

Hypercharge calculated from electric charge and weak isospin.

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Qe (electric charge)

Quantum number for electric charge.

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T3 (weak isospin)

Third component of weak isospin.

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nYw equation

Equation defining nYw , including gravitational coupling.

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Gravitational coupling

Interaction strength of gravity.

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B(baryon number)

Quantum number for baryons.

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L(lepton number)

Quantum number for leptons.

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nup/nup̅

Unstable particles and their antiparticles.

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k

Calculated using the reciprocal Fibonacci constant.

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Ψ

Reciprocal Fibonacci constant (3.3598856...).

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c1, c2, c3, c4

Parameters in equations.

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Qf (quark flavor)

Quantum number for quark flavors.

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Lf (lepton flavor)

Quantum number for lepton flavors.

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I3 (isospin)

Third component of isospin.

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Study Notes

Explaining Ratios of Masses of Leptons and Quarks

  • Three generations or families of leptons and quarks exist.
  • The known mass ratios of these particles within their generations are explained.
  • The article attempts to solve the problem of Yukawa couplings as arbitrary parameters in the Standard Model Higgs mechanism.
  • A new methodology based on the running of the fine-structure constant, quantum numbers, and the Weinberg angle is introduced to explain Yukawa couplings of all leptons and quarks.
  • Predictions are made for left-chiral neutrino mass eigenstates.
  • Upper limits are provided for right-chiral neutrino mass eigenstates.

Standard Model Scalar Potential

  • The Standard Model scalar potential is given by V(Φ) = m²Φ†Φ + λ(Φ†Φ)² where:
    • Φ is a self-interacting SU(2) complex doublet.
    • Y = 1 (weak hypercharge)
    • V(Φ) is the most general renormalizable scalar potential.
    • A negative quadratic term results in a non-zero vacuum expectation value (v).
    • v ≈ 246.22 GeV.
    • GF is the Fermi coupling constant

Higgs Lagrangian

  • The Higgs Lagrangian relates the Higgs field to gauge fields (Wμ and Bμ).
  • g and g' represent SU(2)₁ and U(1)y gauge couplings.
  • The Lagrangian includes the covariant derivative and potential terms.

Yukawa Lagrangian

  • Lepton masses are defined by a free parameter (Yukawa Coupling af).
  • The Higgs field couples with fermions with a Yukawa coupling defined.
  • The Higgs mechanism does not predict fermion masses directly.

Higgs-Yukawa Family/Generation Equation

  • A new equation for Yukawa couplings is introduced.
  • It doesn't depend on the Higgs VEV and explains mass ratios of the three generations.
  • The equation is presented:
    • It involves the running fine-structure constant (a(Q)).
    • N representing generation number.
    • θw(Q) representing the running Weinberg angle.
    • (1 + Δqf) is the correction factor for unstable leptons.
    • It includes the quantum numbers and fermion flavour.

Leptonic Solutions

  • All leptons have a lepton quantum number (L).
  • Left-chiral leptons have a weak hypercharge (Yw = -1) while right-chiral, charged leptons have a hypercharge of -2.
  • Right-chiral neutrinos are "sterile," lacking weak hypercharge, weak isospin, and charge.

Charged Leptons

  • All charged leptons have a charge quantum number (Qe).
  • Left-chirality has weak isospin (T3 = 1/2).
  • Right-handed charged leptons have zero weak isospin.
  • Formula for electron, muon, and tau Yukawa couplings are shown.

Neutrino Solutions

  • All neutrinos have a charge of 0.
  • Left-chiral neutrinos have weak isospin (T3 = 1/2).
  • Right-handed, or sterile neutrinos (if present) have weak isospin = 0 and do not have charge.
  • Two formulae are presented for Left and Right neutrinos with their predictions of masses.

Quark Solutions

  • Quarks have a baryon quantum number (B = 1/3 or -1/3 ).
  • Up-type quarks have weak hypercharge (Yw = 1/3), while down-type have (Yw = -2/3).
  • Formulas for down (d), strange (s), bottom (b) and up (u), charm (c), top(t) type quark Yukawa couplings and masses are presented with their respective quantum numbers.

References

  • Citations to numerous Physics publications and articles.

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